It is well known that in some cars and mobile platforms, each wheel is driven independently. When such vehicles are steered, the translational velocity of each wheel is typically dependent upon the velocities of each of the remaining wheels. Due to the interdependency of each of the velocities of the individual wheels, as the operator of the vehicle continues to control the drive wheels, it is well known that errors occur and the wheels slip, an error occurring when a wheel is driven at a lower or higher velocity than required.
It is well known that when a vehicle is driven in an arcuate path, the motion of each wheel is constrained. The wheel velocity divided by the radius to the center of rotation must be the same for all wheels. Further, each wheel must be instantaneously traveling in a path tangential to a circle concentric with circles about which each of the other respective wheels are traveling.
It is well known that a vehicle with two drive wheels has one constraint and one degree of freedom. A vehicle with four drive wheels has three constraints and one degree of freedom. For a vehicle with n drive wheels, it follows that there are (n-1) constraints and one degree of freedom. The degree of freedom present in each of the above cases may be parameterized by a new scalar variable termed the pseudovelocity, while the (n-1) constraints are imposed on the values of the wheel translational velocities.
Several articles have been published which discuss a control architecture for constrained mechanical systems. Typical of these articles are M. A. Unseren, "Rigid Body Dynamics and Decoupled Control Architecture for Two Strongly Interacting Manipulators," Robotica, pp. 421-430 (1991), Vol. 9; H. Faessler, "Manipulators Constrained by Stiff Contact: Dynamics, Control, and Experiments," The International Journal of Robotics Research, pp. 40-58 (1990), Vol. 9, No. 4; and R. K. Kankaanranta and H. N. Koivo, "Dynamics and Simulation of Compliant Motion of a Manipulator," IEEE Journal of Robotics and Automation, Vol. 4, No. 2, pp. 163-173 (1988).
Of these, Kankaanranta and Koivo disclose the most material art to the present invention. Kankaanranta and Koivo disclose the application of a control architecture to constrained manipulators. Kankaanranta and Koivo do not disclose the application of such a control architecture for controlling vehicles and other mobile platforms.
It is well known that a wheel is a system that must satisfy a nonholonomic constraint. At each instant, a wheel rolling on a horizontal plane without slipping can move in one only direction. Motion in the orthogonal direction requires maneuvering. An example of the maneuvering required by a nonholonomic platform is the parallel parking of a car, where it is desirable to move the automobile in a direction orthogonal to the wheels. In this example, it is well known that the optimum path is arc-line-arc and is accomplished by turning the wheels to one limit, backing, straightening the wheels, backing, turning the wheels to the other limit, backing, and straightening the wheels.
A mobile platform with steerable wheels can use the steering degrees of freedom to reduce the required maneuvering. For example, a car with four steerable wheels can parallel park by turning the four wheels sideways and moving directly into the parking space. In addition to moving in a line in any direction, a platform with steerable wheels can move in a circle about any center of rotation, which is useful for working around circular objects such as storage drums or tanks.
Several devices have been developed which include independently-controlled wheels. Typical of the art are those devices disclosed in the following U.S. Pat. Nos:
______________________________________ U.S. Pat. No. Inventor(s) Issue Date ______________________________________ 4,541,051 J. Jarret, et al. Sep. 10, 1985 4,674,048 K. Okumura June 16, 1987 4,866,624 S. Nishikawa, et al. Sep. 12, 1989 5,019,984 S. Masaki, et al. May 28, 1991 5,024,285 N. Fujita June 18, 1991 5,085,288 S. Shiraishi, et al. Feb. 4, 1992 5,090,510 K. Watanabe, et al. Feb. 25, 1992 5,157,611 T. Ikeda, et al. Oct. 20, 1992 5,164,903 W. C. Lin, et al. Nov. 17, 1992 ______________________________________
Of these patents, the Jarret ('051) patent is directed toward a vehicle having two steerable drive wheels. The Jarret device includes one or more pairs of non-steerable drive wheels, each driven independently. In such vehicles, when more than one pair of non-steerable drive wheels is provided, motion of the vehicle is limited to straight line translational movement. Therefore, no rotational motion may be accomplished.
The Okumura ('048) device as disclosed includes two non-steerable drive wheels, the translational velocities of each being independent of the other. Due to the lack of constraint on each of the translational wheel velocities, the translational velocity of each wheel pair may vary from each other pair of wheels.
The Nishikawa ('624) patent discloses a four-wheel drive vehicle having a front differential, a rear differential, and a differential between the front and rear pairs of wheels. The differentials provided by Nishikawa serve to remove the constraints from each of the wheels. In such vehicles, all of the wheels are driven by a single motor. A differential system such as incorporated in the Nishikawa vehicle is not desirable in a vehicle wherein each of the wheels is independently actuated.
The Masaki ('984) patent does not disclose a means for sensing or controlling steering angles of the independent drive wheels. Masaki is directed toward slip detection and correction techniques based solely on the sensing and measurement of the wheel rotation rates in order to improve the braking efficiency of a vehicle, considering each wheel as an individual entity.
Fujita ('285) discloses a device which includes two steerable wheels and two non-steerable drive wheels. Fujita requires detecting and correcting the slip of the wheel or wheels and necessitates the sensing of the rotational velocity of the un-driven wheels. However, it is not desirable to require any knowledge of un-driven wheels, as they are preferably included for stability of the vehicle and provide no directional or motivational forces to the vehicle.
The Shiraishi ('288) patent discloses a device which has four wheels, the front pair being driven. Shiraishi provides a means for detecting slippage of a wheel due to discontinuities in the surface over which the vehicle is traveling.
Watanabe ('510), as did Nishikawa ('624) above, discloses a vehicle having four-wheel drive capability which includes a front differential, a rear differential, and a differential between the front and rear wheel pairs. As in other devices cited, the Watanabe device includes a pair of steerable drive wheels and a pair of non-steerable drive wheels. The Watanabe device is capable of translational motion only, and is not capable of rotational motion.
Ikeda ('611) discloses a four-wheeled device capable of either front-wheel drive or rear-wheel drive, but not both. Ikeda controls the torque of each drive wheel to maintain it at a pre-specified reference value. The Ikeda device is not treated as a single constrained mechanical system.
Although in one embodiment of the Lin ('903) patent is disclosed a vehicle which may have four independent drive wheels, Lin assumes that the wheels are pointed forward and the drive speed for each is identical to the drive speed of the others. The Lin disclosure is not directed toward a vehicle having n number of steerable drive wheels, each being constrained and each having a unique target speed. Nor does Lin account for the inter-wheel coupling effects which are quantified by constraints imposed on the translational velocities of each of the wheel pairs in a four-wheel drive system.
Therefore it is an object of the present invention to provide a means to minimize errors and prevent slipping of the individual wheels of a wheeled vehicle having two or more independently-steerable drive wheels, especially when controlling the vehicle to follow a path about a selected center of rotation.
It is another object of the present invention to provide such a means whereby the positioning accuracy of the vehicle is enhanced.
Another object of the present invention is provide such a means which may be adaptable to any type of vehicle wherein a plurality of drive wheels is incorporated, including automobiles and robots.
Still another object of the present invention is to provide a means whereby the translational velocities of all of the wheels in such a vehicle may be controlled as a single unit.